Importance of torsion and invariant volumes in Palatini theories of gravity

Abstract

We study the field equations of extensions of General Relativity formulated within a metric-affine formalism setting torsion to zero (Palatini approach). We find that different (second-order) dynamical equations arise depending on whether torsion is set to zero i) a priori or ii) a posteriori, i.e., before or after considering variations of the action. Considering a generic family of Ricci-squared theories, we show that in both cases the connection can be decomposed as the sum of a Levi-Civita connection and terms depending on a vector field. However, while in case i) this vector field is related to the symmetric part of the connection, in ii) it comes from the torsion part and, therefore, it vanishes once torsion is completely removed. Moreover, the vanishing of this torsion-related vector field immediately implies the vanishing of the antisymmetric part of the Ricci tensor, which therefore plays no role in the dynamics. Related to this, we find that the Levi-Civita part of the connection is due to the existence of an invariant volume associated to an auxiliary metric $h_{\mu \nu }$, which is algebraically related with the physical metric $g_{\mu \nu }$.

14 one-column pages, no figures; v2: some minor changes and typos corrections, new references added

References in corpus (27)

• The Confrontation between General Relativity and Experiment
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Limit to General Relativity in f(R) theories of gravity
• Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
• Bouncing Cosmologies in Palatini $f(R)$ Gravity
• Surface singularities in Eddington-inspired Born-Infeld gravity
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Spherically symmetric spacetimes in f(R) gravity theories
• Dark spinors with torsion in cosmology
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Dynamical Aspects of Generalized Palatini Theories of Gravity
• Re-examination of Polytropic Spheres in Palatini f(R) Gravity
• The Cauchy problem of f(R) gravity
• The interior spacetimes of stars in Palatini f(R) gravity
• Reconstructing f(R) modified gravity from ordinary and entropy-corrected versions of the holographic and new agegraphic dark energy models
• The dynamics of generalized Palatini Theories of Gravity
• D6-branes and torsion
• Semiclassical geons as solitonic black hole remnants
• Torsion Phenomenology at the LHC
• Dirac fields in f(R)-gravity with torsion
• Semiclassical geons at particle accelerators
• Holography in 3D AdS gravity with torsion
• Running coupling in electroweak interactions of leptons from f(R)-gravity with torsion
• Nonsingular electrovacuum solutions with dynamically generated cosmological constant
• Cosmology in Palatini theories of gravity

Cited by in corpus (40)

• Born-Infeld inspired modifications of gravity
• Ghosts in metric-affine higher order curvature gravity
• Geonic black holes and remnants in Eddington-inspired Born-Infeld gravity
• Extended Gauss-Bonnet gravities in Weyl geometry
• Instabilities in Metric-Affine Theories of Gravity
• Geodesic completeness in a wormhole spacetime with horizons
• What is a singular black hole beyond General Relativity?
• Born-Infeld gravity and its functional extensions
• Brane-world and loop cosmology from a gravity-matter coupling perspective
• Unveiling the Dynamics of the Universe
• Born-Infeld-$f(R)$ gravity
• Crystal clear lessons on the microstructure of space-time and modified gravity
• Thick brane in $f(R)$ gravity with Palatini dynamics
• Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-Infeld
• Microscopic wormholes and the geometry of entanglement
• Little Rip, $\Lambda$CDM and singular dark energy cosmology from Born-Infeld-$f(R)$ gravity
• Black holes in five-dimensional Palatini $f(R)$ gravity and implications for the AdS/CFT correspondence
• Dynamical generation of wormholes with charged fluids in quadratic Palatini gravity
• Semiclassical geons at particle accelerators
• Classical resolution of black hole singularities in arbitrary dimension
• Planck scale physics and topology change through an exactly solvable model
• Scalar geons in Born-Infeld gravity
• Varying the Horndeski Lagrangian within the Palatini approach
• Cascading dust inflation in Born-Infeld gravity
• Tensor perturbations in a general class of Palatini theories
• Robustness of braneworld scenarios against tensorial perturbations
• Geodesically complete BTZ-type solutions of $2+1$ Born-Infeld gravity
• Gödel-type solutions within the f(R,Q) gravity
• Stability of non-degenerate Ricci-type Palatini theories
• The quantum, the geon, and the crystal
• Nonsingular electrovacuum solutions with dynamically generated cosmological constant
• Nonsingular black holes in Palatini extensions of General Relativity
• Melvin Universe in Born-Infeld gravity
• A correspondence between $1^{st}$ and $2^{nd}$ order formalism by a metricity constraint
• Energy transfer from space-time into matter and a bouncing inflation from Covariant Canonical Gauge theory of Gravity
• Comparing metric and Palatini approaches to vector Horndeski theory
• Quadratic Palatini gravity and stable black hole remnants
• Non-Riemannian geometry: towards new avenues for the physics of modified gravity
• Horizonless, singularity-free, compact shells satisfying NEC
• Modified gravity in three dimensional metric-affine scenarios